First, a brief overview of Dr. Leymann's observations:
In his research about mobbing (it seems
safe to say that mobbing is a term for group bullying), he found nothing that showed that
victim
personalities caused mobbing, but rather that mobbing causes Post-Traumatic Stress Disorder
(PTSD), which, practically speaking,
changes the victim's personality. Sometimes their orientation
toward life is so drastically changed that they become very
ineffective people, losing their careers. Leymann outlined the stages of mobbing as starting with a conflict
of some sort that is not effectively dealt with (sometimes no fault of the victim, for
example, incommunicative workplace managers). The next stage involves people using
a negative approach to the victim where any one exchange or incident does not seem
very concerning (example: gossip), but, over time, the pattern forms a hostile environment that has the flavor
of retribution toward the victim. There are one to several people involved in this and any number
of bystanders who are aware of what is going on but who do nothing. When and if authorities come in,
they take the side of the majority:
the consensus seems to be that the victim is at fault and the authorities would rather
not get involved and would rather not
take responsibility for effectively managing things, regardless. If the victim seeks psychiatric
help, they are usually seen as paranoid and suchlike because most psychotherapists are not
very familiar with PTSD. The victim falls ill more often
than before
and is eventually ejected from the job after an average of 15 months. They are stigmatized
by the entire sequence, for instance, feeling obsessed with wariness.

Does Holden show the signs of PTSD?

I do not have a degree in psychology or anything like that, but I can read the
diagnoses well enough, I think, and so can anyone. Looking over
the standard PTSD diagnosis
(American Psychiatric Association), I think he fits group C with avoiding stimuli
that can be associated with the trauma via methods 4, 5, and 7 (specifically, he's
uninterested in school and in what the teachers think of him, which I think it's
safe to say are important, he's been expelled by schools for not applying himself;
there is a mismatch between him and most other people; and he tends to
see his future
as having no career or even of dying young  of cancer, pneumonia, or suicide).
I think he also fits group D (arguably even better than he fits group C) as he has
difficulty falling asleep and repeatedly finds it hard to concentrate, gets irritable,
and is vigilant of phonies.
Yes, he shows the signs of PTSD.

A related question is whether, if Holden does have PTSD, was it from a single
traumatic event or from a chronic trauma lasting at least a month (in effect,
the group E permutation)? Basically, why does he have PTSD?
Although he could have repressed memories not mentioned in the book, I'll
assume he mentions every relevant thing. We know about his brother's death
and his other brother's
going to war and coming back shell shocked and changing the way he writes.
I don't think his brother dying is outside of ordinary experience. Since everyone
dies, everyone has to deal with death (in fact, Dr. Leymann died). Also, Holden was 13,
so he was no small child. Further, Allie died of cancer, which I assume his family was
aware of before he died, which means his death was neither violent nor a surprise.
Also note that, although Holden is preoccupied with Allie's death, he is much more preoccupied
with the prevalence of phonies.
Holden remembered being a kid seeing
his brother, D.B., on leave from the war, doing almost nothing but lie
on his bed. Holden said he didn't think he could handle being called up to war. He'd
rather be executed than to go to war (p. 140).
Holden also saw D.B. moving to Hollywood to write
movies as a major change in D.B.s approach to writing (p. 1, 164). Maybe D.B. came back from the
war acting like a phony sometimes (note that other times he earnestly argued about
war poetry, p. 140).
Yet, at both the start and end of the book, Holden mentioned contacts with his brother, but
shows no venom for him (at least nothing remotely like his disdain toward the phonies).
He seems puzzled and angry by D.B.'s change, but
D.B. does not seem to be the center of Holden's apparent PTSD. And even if it were,
I think that seeing D.B. inactive
during leave is not enough outside the ordinary experience to be a single trauma,
and seeing D.B. change and go to Hollywood would seem like a chronic question more
than a chronic trauma.
Now, here's something: at Elkton Hills, Holden heard James Castle fall out the window
to his death and he saw James Castle's dead body, bloody and broken,
wearing his borrowed sweater. He saw people hanging back, inactive, until one teacher carried
James' body away. He saw the killers get off with a mere expulsion.
That's the most traumatic event Holden mentions, which
I envision as tied in with some additional, chronic trauma.

I'm picturing that Holden was mobbed (bullied) in the first
school he was expelled from
(which I'm assuming was Elkton Hills  see notes). I picture Holden as a sensitive kid in
boarding school  perhaps he was new to boarding schools 
being pushed around by
classmates. I imagine it becoming an anxious, hostile situation as time went on. Meanwhile, a
classmate, James Castle, was being mobbed even more than Holden, to the point where James was so
subdued that the teacher rarely called on him and he hardly talked to anyone (p. 171). Then the
mobbers killed James, and, even then, no one but one teacher even wanted
to get near his body and the killers remained free in society (p. 170).

James' body was lying
in blood, wearing Holden's sweater. The impression Holden could have been struck with:
"that could have been me, if things were just a
little different, or when things got bad enough for me here." His sense of security in the "nice" school
society could have evaporated.

Indeed, what we know about Holden is that he basically quit
Elkton Hills (p. 13). Mr. Antolini kept in touch with Holden and his parents
and was concerned about his progress (p. 180). I envision Holden as traumatized by this
classmate's death. The one teacher who crossed the line and picked up James' body also got
involved with Holden's progress (p. 170, 180), but the rest of the school did not. Holden
changed schools two more times but
didn't keep up with his studies (p. 4, 13, Holden had no objection to Mr. Spencer's
characterizing his problems at the Whooton school as similar to his problems at Pencey).

The last school we know about Holden going to was, Pencey. Several times, he
mentions Elkton Hills and the Whooton School as previous boarding schools he'd attended.
It's not made absolutely clear which school was the first of those.

Elkton Hills seems to be farther back in time.
In the time since Holden left Elkton Hills, Mr. Antolini also left there, moved to New York [p. 173],
frequently visited the Caulfields to follow Holden's progress [p. 180], got
married [p. 180], and is well settled in marriage. Mr. Antolini also seems wry
about the news that Holden got kicked out of Pencey, not like it was a new thing for
Holden to get kicked out of a school [p. 174]. Meanwhile, the Whooton school seemed
more recent and Holden seems
older in the Whooton period: boys dated there [p. 136], there were sex talks [p. 143], he
drank there at least once [p. 90], and he was studying some of the same material as at Pencey
[Beowulf, Lord Randal My Son, p. 10].
Finally, when Mr. Spencer mentions Holden's failing
at other schools, he mentions the Whooton school first and then Elkton Hills, possibly
as a way to underline his sarcastic point [p. 13].
The way I see that is Spencer first mentioned the most recent school and then the previous
school  that's the most natural way to speak, referring back, then farther back into
the past.

Imagine learning that a group of classmate bullies could drive someone
to their death yet still almost no one would want to get near the victim.
Imagine that the bullies would only get expelled like poor performers, instead of going to jail
like killers (p. 170).
I picture Holden coming to view the characters
of the killers as a bunch of self-impressed, alienating phonies pushing people
around to get performances out of them while everyone else stands by doing
little or nothing. James Castle was killed because he referred to
a very conceited guy as a very conceited guy and wouldn't take it back (p. 170).

Since the authorities in charge didn't come down on the bullies as killers, Holden also came to
doubt their authority. The Elkton Hills headmaster, was a huge phony
(p. 13-14).

Holden came to question almost everyone's integrity and trustworthiness.
When he comes to the Whooton
school, he observes how Luce controls conversations to maximize the impression he
makes: Luce, a student advisor, does sex talks to impress the younger boys and then
tries to separate everyone so no one can follow up with any smarter remarks (p.
143, 147). When
Holden goes to Pencey, he observes what a clean cut guy Stradlater looks like to the public
eye but what a self-obsessed slob he is in private (p. 27). Holden observes how everyone cuts Ackley
out (basically mobbing him, p. 167) as if they're clearly superior when in fact they're
mean guys and arguably inferior. Holden sees how a mean guy's mother cares more about how her voice sounds
than about seriously asking herself what sort of son she has (p. 54-8). I could go on, but
there is all too much
insincerity and Holden is honestly uninterested in engaging in such a
superficial, alienating society.
(He finds children a proven exception to that.) He dreams of living a more rustic,
sure way of life (p. 132-3, 198-9, 204-5).

Getting back to the first question a bit, does Holden have a form of
PTSD specifically noted
in victims of mobbing/bullying? I think Holden
fits the last one ("additional symptoms that indicate that the
patient has resigned himself or herself to the situation") because Holden arguably has
all three traits: wishes
to get away from people (p. 198, 166), generally feels alienated from society, and a
generally cynical attitude toward the world.
(A compelling note is a trait from the first category.
"Hypersensitivity with respect to injustices and a constant identification with the
suffering of others in an almost compulsory manner" [emphasis added].
It certainly describes his feeling charitable toward and sorry for so many people [the nuns,
Mr. Spencer, Thurmer's daughter,
girls in general, Ernie; p. 111-113, 15, 3, 123, 84], even being generous to people he
didn't even like [inviting Ackley along on an outing and buying
tons of drinks for the witches at the bar; 36, 75].)

Looking at the stages of mobbing, Holden's ongoing lack of interest in school and
society, and indeed, his acceptance at the end of letting things go the way
they go, seems to point to his being entrenched in PTSD. In fact, Leymann's repeatedly
referring to the practical personality change as "permanent" is a disturbing prognosis
for Holden's future. Indeed, the last stage (in the worse cases, at least) is the person losing
their career, never able to really engage again. At the end of Catcher, Holden's
almost Que
Sera Sera attitude seems somewhat
reassuring and even amusing, but many readers are left with a lingering
question of what will become of him.

Are Holden's fans suffering from PTSD?

I don't know how many people have PTSD, but I suspect the percentage is high. Not only
are there concentration camp and battle survivors and earthquake survivors in the
population, but up to half of the people in our culture were stressed by possibly not being
securely attached to their caregiver in infancy and childhood
(The Highly Sensitive Person, by Elaine N. Aron, p. 43, 33-35).
This is arguably a chronic trauma.
Further, consider how many people have been mobbed or bullied for at least one month in junior
high school and high school, possibly getting PTSD from that experience. (A conundrum:
if more than
half of a population has trauma, does trauma become not outside the
ordinary experience? I think it makes little difference.
I think an overwhelming majority of people in Afghanistan
during the Taliban rule had such trauma, but I imagine that PTSD is very widespread there.)

The Catcher in the Rye is
an unusual first person narrative, of someone who arguably has PTSD, told very vividly
and with humor. It would be a very popular book in a world with a large
number of people with PTSD  a world with a prevalence of traumas.
Of course we know that Salinger's book is very popular indeed.
It can be seen
as resonating with a lot of people who relate to Holden either through having PTSD
themselves or through understanding their PTSD neighbors through his eyes.
And, of course, there's
the wicked sense of humor and the easy read that captivates almost all other
readers.
The time period, culture, and class don't seem to matter much:
the book has fans in many countries and all classes.